Academics > Computer Modeling of Dynamical Systems with Distributed Parameters (am)

Computer Modeling of Dynamical Systems with Distributed Parameters (am)

Type: For the student's choice

Department: applied mathematics

Curriculum

SemesterCreditsReporting
103Setoff

Lectures

SemesterAmount of hoursLecturerGroup(s)
1016Associate Professor M. V. ShcherbatyyPMp-51m, PMp-52m

Laboratory works

SemesterAmount of hoursGroupTeacher(s)
1016PMp-51mAssociate Professor M. V. Shcherbatyy, Associate Professor V. M. Biletskyj
PMp-52mAssociate Professor M. V. Shcherbatyy, Associate Professor V. M. Biletskyj

Course description

Brief abstract of the discipline
The course is focused on familiarizing students with methods and techniques for modeling and analyzing dynamical systems whose behavior is considered in the space-time domain. The main emphasis is placed on parabolic equations, in particular on diffusion and reaction-diffusion models. The course also includes the qualitative analysis of dynamical systems, considering first ordinary differential equations as a preliminary preparation for the analysis of systems with distributed parameters. Examples of problems from various fields (including population dynamics, epidemiology, and other systems) demonstrate the material in this course.

The aim of the course is to provide students with knowledge and skills in the field of:
– computer modeling and qualitative analysis of dynamic systems with distributed parameters, in particular, systems with partial differential equations of parabolic type;
– use of computer mathematics systems (e.g., Matlab, Octave) to study the formulated mathematical models.

Recommended Literature

Basic literature
1. Kuttler C. Reaction-Diffusion equations with applications. Sommersemester, 2011.
2. Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology. Springer, 2012.
3. Volpert V. Elliptic Partial Differential Equations. Volume 2: Reaction-Diffusion Equations. Springer Basel, 2014.
4. Lam K-Y, Lou Y. Introduction to Reaction-Diffusion Equations. Theory and Applications to Spatial Ecology and Evolutionary Biology. Springer, 2022.
5. Пічкур В. В., Капустян О. В., Собчук В. В. Теорія динамічних систем. Луцьк, Вежа-Друк, 2020.
6. Хусаінов Д.Я., Харченко І.І., Шатирко А.В. Введення в моделювання динамічних систем. Київський національний університет імені Тараса Шевченка, 2010.

Additional literature
7. Іванків К.С., Щербатий М.В. Математичне моделювання біологічних та еколого-економічних процесів. Львів, Видавничий центр ЛНУ імені Івана Франкаб 2005.
8. Perko L. Differential Equations and Dynamical Systems. Springer, 2001.
9. Quarteroni A. Numerical Models for Differential Problems. Springer, 2017.
10. Quarteroni A., Saleri F., Gervasio P. Scientific Computing with MATLAB and Octave. Springer, 2014.
11. MATLAB Homepage: http://www.mathworks.com/products/matlab/.
12. GNU Octave Homepage: http://www.gnu.org/software/octave/